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No three numbers use all digits

Source: 2012 Indonesia Round 2.5 TST 4 Problem 2

May 31, 2012
combinatorics proposedcombinatorics

Problem Statement

Let TT be the set of all 2-digit numbers whose digits are in {1,2,3,4,5,6}\{1,2,3,4,5,6\} and the tens digit is strictly smaller than the units digit. Suppose SS is a subset of TT such that it contains all six digits and no three numbers in SS use all six digits. If the cardinality of SS is nn, find all possible values of nn.
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